{"id":"https://openalex.org/W2569171899","doi":"https://doi.org/10.1109/cdc.2016.7798694","title":"Numerical methods for stochastic differential equations in the Stiefel manifold made simple","display_name":"Numerical methods for stochastic differential equations in the Stiefel manifold made simple","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2569171899","doi":"https://doi.org/10.1109/cdc.2016.7798694","mag":"2569171899"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2016.7798694","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798694","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://handle.unsw.edu.au/1959.4/unsworks_47004","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018011442","display_name":"Goran Marjanovic","orcid":"https://orcid.org/0000-0003-2016-2384"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Goran Marjanovic","raw_affiliation_strings":["School of Electrical Engineering and Telecommunications, University of New South Wale, Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Telecommunications, University of New South Wale, Sydney, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056263605","display_name":"Marc J. Piggott","orcid":"https://orcid.org/0000-0001-5576-8867"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Marc J. Piggott","raw_affiliation_strings":["School of Electrical Engineering and Telecommunications, University of New South Wale, Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Telecommunications, University of New South Wale, Sydney, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091154507","display_name":"Victor Solo","orcid":"https://orcid.org/0000-0002-5123-7708"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Victor Solo","raw_affiliation_strings":["School of Electrical Engineering and Telecommunications, University of New South Wale, Sydney, Australia"],"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Telecommunications, University of New South Wale, Sydney, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018011442"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":null,"apc_paid":null,"fwci":2.2813,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.88213244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"2853","last_page":"2860"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stiefel-manifold","display_name":"Stiefel manifold","score":0.977419376373291},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.7240903973579407},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6111555695533752},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5547156929969788},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5305797457695007},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.4476699233055115},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.44463637471199036},{"id":"https://openalex.org/keywords/manifold-alignment","display_name":"Manifold alignment","score":0.43646979331970215},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.4362525939941406},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.42572298645973206},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4205816984176636},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4201195240020752},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32281821966171265},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.293124794960022},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.23768359422683716},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23174989223480225},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14074021577835083},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07258737087249756},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06428349018096924},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.06406930088996887}],"concepts":[{"id":"https://openalex.org/C612670","wikidata":"https://www.wikidata.org/wiki/Q7616373","display_name":"Stiefel manifold","level":2,"score":0.977419376373291},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.7240903973579407},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6111555695533752},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5547156929969788},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5305797457695007},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.4476699233055115},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.44463637471199036},{"id":"https://openalex.org/C153120616","wikidata":"https://www.wikidata.org/wiki/Q17068315","display_name":"Manifold alignment","level":4,"score":0.43646979331970215},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.4362525939941406},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.42572298645973206},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4205816984176636},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4201195240020752},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32281821966171265},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.293124794960022},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.23768359422683716},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23174989223480225},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14074021577835083},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07258737087249756},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06428349018096924},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.06406930088996887},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2016.7798694","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798694","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:unsworks.unsw.edu.au:1959.4/unsworks_47004","is_oa":true,"landing_page_url":"http://handle.unsw.edu.au/1959.4/unsworks_47004","pdf_url":null,"source":{"id":"https://openalex.org/S4377196481","display_name":"UNSWorks (UNSW Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31746571","host_organization_name":"UNSW Sydney","host_organization_lineage":["https://openalex.org/I31746571"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:unsworks.library.unsw.edu.au:1959.4/unsworks_47004","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.4/unsworks_47004","pdf_url":null,"source":{"id":"https://openalex.org/S4306401737","display_name":"UNSWorks (University of New South Wales, Sydney, Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40053085","host_organization_name":"Australian Defence Force Academy","host_organization_lineage":["https://openalex.org/I40053085"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, USA, 2016-12-12 - 2016-12-14","raw_type":"http://purl.org/coar/resource_type/c_5794"}],"best_oa_location":{"id":"pmh:oai:unsworks.unsw.edu.au:1959.4/unsworks_47004","is_oa":true,"landing_page_url":"http://handle.unsw.edu.au/1959.4/unsworks_47004","pdf_url":null,"source":{"id":"https://openalex.org/S4377196481","display_name":"UNSWorks (UNSW Sydney)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31746571","host_organization_name":"UNSW Sydney","host_organization_lineage":["https://openalex.org/I31746571"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1489270186","https://openalex.org/W1530474308","https://openalex.org/W1544770838","https://openalex.org/W1551148884","https://openalex.org/W1561367079","https://openalex.org/W1583323312","https://openalex.org/W1588770196","https://openalex.org/W1810520904","https://openalex.org/W1972803533","https://openalex.org/W1979674792","https://openalex.org/W1981041413","https://openalex.org/W1992278142","https://openalex.org/W1994384777","https://openalex.org/W2006409769","https://openalex.org/W2009977354","https://openalex.org/W2020710505","https://openalex.org/W2044640615","https://openalex.org/W2045512849","https://openalex.org/W2055843842","https://openalex.org/W2061356302","https://openalex.org/W2094210680","https://openalex.org/W2118708484","https://openalex.org/W2120516507","https://openalex.org/W2131838761","https://openalex.org/W2133318743","https://openalex.org/W2140393629","https://openalex.org/W2144707556","https://openalex.org/W2268373246","https://openalex.org/W2292394767","https://openalex.org/W2515882314","https://openalex.org/W2911730943","https://openalex.org/W2915178317","https://openalex.org/W3038054700","https://openalex.org/W3102195404","https://openalex.org/W3102336164","https://openalex.org/W4205510932","https://openalex.org/W4229928878","https://openalex.org/W4231021340","https://openalex.org/W4243961535","https://openalex.org/W4255754126","https://openalex.org/W4300831640"],"related_works":["https://openalex.org/W4399521585","https://openalex.org/W1521148900","https://openalex.org/W4226388829","https://openalex.org/W2780226079","https://openalex.org/W2070844282","https://openalex.org/W1983594265","https://openalex.org/W1491593166","https://openalex.org/W1602288242","https://openalex.org/W2089827361","https://openalex.org/W2129233184"],"abstract_inverted_index":{"Several":[0],"engineering":[1,92],"applications":[2],"require":[3],"numerical":[4],"schemes":[5,38,53],"for":[6,62],"the":[7,15,33,44,55,68,80],"simulation":[8],"of":[9,18,32],"stochastic":[10],"differential":[11],"equations":[12],"(SDEs)":[13],"on":[14,54,67,79],"Stiefel":[16,34,56,81],"manifold":[17,35,45],"n":[19,96],"\u00d7":[20],"p":[21,99],"real":[22],"matrices":[23],"with":[24,95],"orthonormal":[25],"columns":[26],"(n":[27],"\u2265":[28],"p).":[29],"The":[30,83],"geometry":[31],"causes":[36],"classical":[37],"to":[39,76,90],"fail,":[40],"as":[41],"they":[42],"leave":[43],"after":[46],"one":[47],"time":[48],"step.":[49],"Motivated":[50],"by":[51],"deterministic":[52],"manifold,":[57],"we":[58],"develop":[59],"a":[60],"scheme":[61,71],"SDEs":[63],"which":[64],"always":[65],"remains":[66],"manifold.":[69,82],"Our":[70],"can":[72],"be":[73],"easily":[74],"applied":[75],"any":[77],"SDE":[78],"derivation":[84],"is":[85],"direct":[86],"and":[87],"made":[88],"accessible":[89],"an":[91],"audience.":[93],"Simulations":[94],"=":[97,100],"1000,":[98],"10":[101],"are":[102],"provided.":[103]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3}],"updated_date":"2025-11-25T21:42:39.735039","created_date":"2017-01-13T00:00:00"}